1. **State the problem:** Kevin wants to buy pencils at P4.50 each and has no more than P55.00 to spend. 2. **Define variables:** Let $x$ be the number of pencils Kevin can buy. 3. **Set up inequality:** The total cost should not exceed P55.00, so: $$4.50x \leq 55$$ 4. **Solve inequality:** Divide both sides by 4.50: $$x \leq \frac{55}{4.50}$$ 5. **Calculate:** $$x \leq 12.222\ldots$$ 6. **Interpret result:** Since Kevin cannot buy a fraction of a pencil, the greatest whole number he can buy is 12. 7. **Final answer:** Kevin can buy **12 pencils**.